Comparison Principle for Elliptic Equations with Mixed Singular Nonlinearities

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by{−Δpu=fuγ+guqinΩ,u=0on∂Ω, where Ω is an open bounded subset of ℝN where Ω is an open bounded subset of ℝN, Δpu := ÷(|∇u|p− 2∇u) is the usual p-Laplacian operator, γ ≥ 0 and 0 ≤ q ≤ p − 1; f and g are nonnegative functions belonging to suitable Lebesgue spaces

Spreading equilibria under mildly singular potentials: pancakes versus droplets

We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive singularity at short ranges, global minimizers are compactly supported and display a microscopic contact angle of π/ 2. Depending on the form of the potential, the macroscopic shape can either be droplet-like or pancake-like, with a transition profile between the two at zero spreading coefficient for purely repulsive potentials. These results generalize, complete, and give mathematical rigor to de Gennes’ formal discussion of spreading equilibria. Uniqueness and non-uniqueness phenomena are also discussed

Shape programming of a magnetic elastica

We consider a cantilever beam which possesses a possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts upon the beam by means of a distributed couple that pulls the magnetization towards its direction. Given a list of target shapes, we look for a design of the magnetization profile and for a list of controls such that the shapes assumed by the beam when acted upon by the controls are as close as possible to the targets, in an averaged sense. To this effect, we formulate and solve an optimal design and control problem leading to the minimization of a functional which we study by both direct and indirect methods. In particular, we prove that minimizers exist, solve the associated Lagrange-multiplier formulation (besides non-generic cases), and are unique at least for sufficiently low intensities of the controlling magnetic fields. To achieve the latter result, we use two nested fixed-point arguments relying on the Lagrange-multiplier formulation of the problem, a method which also suggests a numerical scheme. Various relevant open question are also discussed

Study And Optimization Of Palm Wood Mechanical Properties By Alkalazition Of The Natural Fiber

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A Circuit-Based Approach to Simulate the Characteristics of a Silicon Photovoltaic Module With Aging

The aging of photovoltaic modules results inevitably in a decrease of their efficiency all through their lifetime utilization. An approach to simulate the evolution of electrical characteristics of a photovoltaic module with aging is presented. The photovoltaic module is modeled by an equivalent electrical circuit whose components have time-dependent characteristics determined under accelerated tests. By entering sun irradiance and temperature, I–V and P–V curves as well as efficiency evolution can be simulated over years assuming equivalent time. The methodology is applied for the case of a monocrystalline photovoltaic module modeled by a one-diode circuit and aging laws are determined with experimental results of damp heat (DH) tests 85 °C/85% RH performed by Hulkoff (2009, “Usage of Highly Accelerated Stress Test (HAST) in Solar Module Aging Procedures,” M.S. thesis, Chalmers University of Technology, Göteborg, Sweden). A power degradation rate of 0.53%/yr is found. A parametric study shows that the rundown of optical transmittance of the upper layers with aging has the most important impact by reducing the initial efficiency by 11.5% over a 25-year exposure contrary to electrical degradations which cause a decrease of 1.85% of the initial efficiency

Accessible opera : overcoming linguistic and sensorial barriers

The desire to make media available for all has been rapidly accepted and implemented by most European countries. Opera, as one of the many audiovisual representations, also falls under the category of production which needs to be made accessible and this article aims to analyse how opera has gone through a complete transformation to become a cultural event for all, overcoming not only linguistic but also sensorial barriers. The first part of the article analyses the various forms of translation associated with opera and the main challenges they entail. The second presents different systems used to make opera accessible to the sensorially challenged, highlighting their main difficulties. Examples from research carried out at the Barcelona's Liceu opera house are presented to illustrate various modalities, especially audio description. All in all, it is our aim to show how translated-related processes have made it possible to open opera to a wider audience despite some initial reluctance

Asymptotic behavior and existence of solutions for singular elliptic equations

We study the asymptotic behavior, as γ tends to infinity, of solutions for the homogeneous Dirichlet problem associated with singular semilinear elliptic equations whose model is -Δu=f(x)uγinΩ,where Ω is an open, bounded subset of RN and f is a bounded function. We deal with the existence of a limit equation under two different assumptions on f: either strictly positive on every compactly contained subset of Ω or only nonnegative. Through this study, we deduce optimal existence results of positive solutions for the homogeneous Dirichlet problem associated with -Δv+|∇v|2v=finΩ

Regularizing effect for some p-Laplacian systems

We study existence and regularity of weak solutions for the following p-Laplacian system −Δpu+Aφθ+1|u|r−2u=f,u∈W01,p(Ω),−Δpφ=|u|rφθ,φ∈W01,p(Ω),where Ω is an open bounded subset of RN(N≥2), Δpv≔div(|∇v|p−2∇v) is the p-Laplacian operator, for 10, r>1, 0≤

Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data

We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is {-Δpu=H(u)μinΩ,u>0inΩ,u=0on∂Ω.Here Ω is an open bounded subset of RN (N≥ 2), Δ pu: = div (| ∇ u| p-2∇ u) (1 < p< N) is the p-laplacian operator, μ is a nonnegative bounded Radon measure on Ω and H(s) is a continuous, positive and finite function outside the origin which grows at most as s-γ, with γ≥ 0 , near zero

Alkaline Treatment Effect on Mechanical Properties of Date palm Wood Fiber

The date Palm tree (Phoenix dactylifera L.) is a providential tree for oases inhabitants, growing in wild state around the Mideterranean North Africa and dry areas. In the past it was used as building material because of its mechanical and hydrous qualities. The use of such a fibrous plant in cementitious matrix leads to lightweight materials with very attractive tensile behavior that can be used as advantageous filling materials for structures. This paper is focused on the optimisation of mechanical properties of this kind of materials by a prior alklaline treatment of the Date palm fiber before its using as reinforcement in a given matrix. The treatment was carried out using sodium hydroxide (NaOH) solution at three different concentration 0.5%, 0.75 % et 1 % NaOH, we submit after that the untreated and treated specimens to a thermogravemetric analysis (TGA) to measure the influence of soda treatment on the mass loss. Afterward, the samples were teseted for mechanical properties dermination. Consistent results were obtained for tensile strength and young modulus, which indicates that the NaOH treatment led to a change in the chemical composition of the Palm fiber and succeeded to improve its mechanical properties and therfore proved the effectiveness of the treatment